Recall that \(a^{\langle k \rangle } = |a|^k \operatorname{sgn}a\) , so \(F_p\)  is the second order Taylor remainder of the convex function \(b\mapsto |b|^p\) . It is therefore an instance of Bregman divergence [1]} and, indeed, we have
\(\tfrac{1}{2}(F_p(a,b) + F_p(b,a)) = H_p(a,b) := \tfrac{p}{2} (a^{\langle p-1\rangle } - b^{\langle p-1 \rangle })(a-b).\) 
